# pymor.algorithms.lrradi¶

## Module Contents¶

pymor.algorithms.lrradi.hamiltonian_shifts(A, E, B, R, K, Z, shift_options)[source]

Compute further shift parameters for low-rank RADI iteration.

Compute Galerkin projection of Hamiltonian matrix on space spanned by last few columns of $$Z$$ and return the eigenvalue of the projected Hamiltonian with the most impact on convergence as the next shift parameter.

See , pp. 318-321.

Parameters

A

The Operator A from the corresponding Riccati equation.

E

The Operator E from the corresponding Riccati equation.

B

The VectorArray B from the corresponding Riccati equation.

R

A VectorArray representing the currently computed residual factor.

K

A VectorArray representing the currently computed iterate.

Z

A VectorArray representing the currently computed solution factor.

shift_options

The shift options to use (see ricc_lrcf_solver_options).

Returns

shifts

A NumPy array containing a set of stable shift parameters.

Compute initial shift parameters for low-rank RADI iteration.

Compute Galerkin projection of Hamiltonian matrix on space spanned by $$C$$ and return the eigenvalue of the projected Hamiltonian with the most impact on convergence as the next shift parameter.

See , pp. 318-321.

Parameters

A

The Operator A from the corresponding Riccati equation.

E

The Operator E from the corresponding Riccati equation.

B

The VectorArray B from the corresponding Riccati equation.

C

The VectorArray C from the corresponding Riccati equation.

shift_options

The shift options to use (see ricc_lrcf_solver_options).

Returns

shifts

A NumPy array containing a set of stable shift parameters.

Returns available Riccati equation solvers with default solver options.

Parameters

hamiltonian_shifts_init_maxiter
hamiltonian_shifts_init_seed
hamiltonian_shifts_subspace_columns

Returns

A dict of available solvers with default solver options.

pymor.algorithms.lrradi.solve_ricc_lrcf(A, E, B, C, R=None, trans=False, options=None)[source]

Compute an approximate low-rank solution of a Riccati equation.

See pymor.algorithms.riccati.solve_ricc_lrcf for a general description.

This function is an implementation of Algorithm 2 in .

Parameters

A

The Operator A.

E

The Operator E or None.

B

The operator B as a VectorArray from A.source.

C

The operator C as a VectorArray from A.source.

R

The matrix R as a 2D NumPy array or None.

trans

Whether the first Operator in the Riccati equation is transposed.

options

The solver options to use. (see ricc_lrcf_solver_options)

Returns

Z

Low-rank Cholesky factor of the Riccati equation solution, VectorArray from A.source.